A Modification to the Discrete $l_1 $ Linear Approximation Algorithm of Barrodale and Roberts

L1 Norm Based Computational Algorithms

“…It has been shown that the dual approach is superior to primal one if a good dual feasible solution is readily available (see also, Steiger (1980)). Banks and Taylor (1980) suggest a modification of Barrodale and Roberts (1973) algorithm. The objective function is altered to include magnitudes of the elements of both errors and solution vectors.…”

Statistical computing support for Lp estimation in augmented linear models under linear inequality restrictions

“…Marquardt (1970) summarized some results on Ridge Regression and emphasized that the ridge estimate overcomes a serious deficiency of the least squares estimate by reducing the Euclidean length of the estimate in the parameter space. Banks and Taylor (1980) used the least absolute deviation criterion in the augmented linear models to fit seismic processing data. They reported excellent results in goodness of fit.…”

“…as X Approaches Zero for the Case p = 1 Banks and Taylor (1980) applied the least absolute deviation technique with the augmented linear model to geophysical problems involving seismic processing. They modified the sinçlex method of Barrodale and Roberts (1973) so that the computer memory requirement of the method is reduced in order to make it more efficient to handle large scale seismic processing problem.…”